Consistent Fusion of MADOCA-PPP and PPP-B2b SSR Corrections for Robust Real-Time PPP

Real-time precise point positioning (PPP) is increasingly supported by open satellite-broadcast state-space representation (SSR) services, yet standalone operation with a single service remains vulnerable to limited constellation support, correction outages, latency variations, and service-dependent modeling inconsistencies. In the Asia-Pacific region, MADOCA-PPP and PPP-B2b provide two publicly accessible and complementary SSR sources, but their consistent fusion before user-level PPP estimation remains insufficiently investigated. This paper proposes a correction-domain fusion framework that combines MADOCA-PPP and PPP-B2b orbit and clock corrections before PPP estimation, rather than merging final positioning solutions. Inter-service discrepancies and unknown cross-correlations are handled by a bias-state-aware structured covariance intersection strategy, in which the relative weighting is derived from the respective correction information (inverse variance), preserving statistical consistency and avoiding overconfident fusion. A unified multi-GNSS PPP scheme further supports signal-priority harmonization, broadcast-ephemeris adaptation, correction-age control, and GLONASS inter-frequency and differential code bias handling. Static-station per-epoch (pseudo-kinematic) and offshore kinematic experiments validate the framework. In the static-station test, fusion raised the mean number of valid satellites from 21.98 and 14.98 to 26.56 and improved the horizontal RMS to 0.033 m—better than either standalone service (0.037 m, 0.079 m)—confirming a genuine combination rather than source selection, while the 3D RMS (0.068 m) matched the best standalone service (0.066 m). In the offshore test, fusion achieved the best overall accuracy (0.232 m horizontal, 0.290 m 3D, versus 0.332 m and 0.313 m for the standalone services) and the most satellites (25.4). It also degraded most slowly with increasing elevation cut-off, outperforming both services about threefold at 40°. A normalized-innovation-squared check confirmed the fused covariance is consistent and not overconfident (median ≈ 1.1; within the 99% bound in 100% of epochs). Under single-service outages from 30 s to 600 s, fusion maintained 100.0% availability, confirming its advantage in redundancy, continuity, and resilience.